Form input passing parameter to a wrong url

I'm trying to make my form pass a parameter to a link like this :

index.php?action=2&parameter=value

Instead, all it does is pass the parameter like this:

index.php?parameter=value

This is my code :

<form class="navbar-form navbar-left" action="index.php?action=2" method="get" name="search">
  <div class="form-group">
      <input type="text" class="form-control" placeholder="put something here...." name="search" width="100">
  </div>
  <button type="submit" class="btn btn-default">search</button>
</form>

The form is located in my index.php?action=2 template but is passing the parameter back to the original index.php file instead of index.php?action=2 file.

I want to use the parameter later as a $_GET with few more parameters in order to search and sort the data taken from DB. The DB php code I wrote works fine, and when I create the link myself it all works nice, but not in the scenario when I try to type the search value in the textbox.

How do I avoid that ?

Thanks in advance!

Edit :

I have a switch in my index.php file which does :

    case 2:
    include "_template/__test.php";
    break;

My form is located in the above __test.php file.